Why doesn't Apple support microSD?

Several reasons:
1) Integrating your storage solution onto the motherboard uses less space than having a microSD slot (so you can have a very slightly smaller phone).
2) In general, read and write speeds will be faster than a microSD card.
3) Allows Apple to make even more profit as they're selling the storage built-in at a massive markup. For example, Apple buys 16 GBs of flash for well under £10 a pop and 32 GBs of flash for under £20 each, but the difference in cost to the buyer is over a £100 between buying a 16 GB iPhone and a 32 GB iPhone.

For the consumer, there are some small advantages, but lack of choice, inability to upgrade and (possible) loss of data if the phone breaks/ has to be sent in for repair are key problems.